Large Matter Effects inνμ→ντOscillations

We show that matter effects change the ${\nu }_{\mu }\to {\nu }_{\tau }$ oscillation probability by as much as 70% for certain ranges of energies and path lengths. Consequently, the ${\nu }_{\mu }\to {\nu }_{\mu }$ survival probability also undergoes large changes. A proper understanding of ${\nu }_{\mu }$ survival rates must consider matter effects in $P_{\mu \tau }$ as well as $P_{\mu e}$. We comment on (a) how these matter effects may be observed and the sign of ${\Delta }_{31}$ determined in atmospheric neutrino measurements and at neutrino factories, and (b) how they lead to heightened sensitivity for small ${\theta }_{13}$.